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If f(x)= [0x−ax−bx+a0x−cx+bx+c0] , then

(A) f(a)=0

(B) f(b)=0

(C) f(0)=0

(D) f(1)=0

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    3 months ago

    This is a Objective Type Questions as classified in NCERT Exemplar

    Sol:

    G i v e n     t h a t     f ( x ) = | 0 x − a x − b x + a 0 x − c x + b x + c 0 |                                                                     f ( a ) = | 0 0 a − b 2 a 0 a − c a + b a + c 0 | E x p a n d i n g     a l o n g     R 1 = ( a − b ) | 2 a 0 a + b a + c |                                                                                               = ( a − b ) [ 2 a ( a + c ) ] = ( a − b ) . 2 a . ( a + c ) ≠ 0                                                               f ( b ) = | 0 b − a 0 b + a 0 b − c 2 b b + c 0 | E x p a n d i n g     a l o n g     R 1 = − ( b − a ) | b + a b − c 2 b 0 |                                                                                             = − ( b − a ) [ ( − 2 b ) ( b − c ) ] = 2 b ( b − a ) ( b − c ) ≠ 0                                                                       f ( 0 ) = | 0 − a − b a 0 − c b c 0 | E x p a n d i n g     a l o n g     R 1 = a | a − c b 0 | − b | a 0 b c |                                                                                             = a ( b c ) − b ( a c ) = a b c − a b c = 0 H e n c e ,     t h e     c o r r e c t     o p t i o n     i s     ( c ) .

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A = [ 1 0 0 0 α β 0 β α ] then α is (if α, β Î I)
A
alok kumar singh

|2A| = 27

8|A| = 27

Now |A| = α2–β2 = 24

α2 = 16 + β2

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(α–β) (α+β) = 16

->α + β = 8 and

α – β = 2

->α = 5 and β = 3

If A = [ 2 1 − 1 2 ] , B = [ 1 0 1 1 ] , C = ABAT and X = AC2AT then |X| is equal to
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alok kumar singh

|A| = 3

|B| = 1

->|C| = |ABAT| = |A|B|A7| = |A|2|B|

= 9

->|X| = |A|C|2|AT|

= 3 * 92 * 3 = 9 * 92 = 729

Matrix A of order 3 × 3 is such that |A| = 2 if n = | a d j ( a d j ( a d j . . . . ( a ) ) ) | ︸ 2 0 2 4   t i m e s  then remainder when n is divided by 9 is
A
alok kumar singh

|A| = 2

a d j ( a d j ( a d j . . . . ( a ) ) ) ? 2 0 2 4   t i m e s = | A | ( n − 1 ) 2 0 2 4            

= | A | ( n − 1 ) 2 0 2 4                                             

= 2 2 2 0 2 4                                          

2 2 0 2 4 = ( 2 2 ) 2 2 0 2 2 = 4 ( 8 ) 6 7 4 = 4 ( 9 − 1 ) 6 7 4             

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2 9 m + 4 ≡ 1 6 ⋅ ( 2 3 ) 3 m ≡ 1 6 ( m o d   9 )

7

If ∫ 0 2 ( 2 x − 2 x − x 2 ) d x = ∫ 0 1 ( 1 − 1 − y 2 − y 2 2 ) d y + ∫ 1 2 ( 2 − y 2 2 ) d y + I     t h e n     I     e q u a l s  
V
Vishal Baghel

∫ 0 2 2 x d x − ∫ 0 2 2 x − x 2 d x = ∫ 0 1 d y − ∫ 0 1 1 − y 2 d y − ∫ 0 2 y 2 2 d y + ∫ 1 2 2 d y + I

⇒ 8 3 − ∫ 0 1 1 − t 2 d t = 1 − 8 6 + 2 + I

I = 1 − ∫ 0 1 1 − t 2 d t

If  ∫ 0 2 ( 2 x − 2 x − x 2 ) d x = ∫ 0 1 ( 1 − 1 − y 2 − y 2 2 ) d y + ∫ 1 2 ( 2 − y 2 2 ) d y + I     t h e n     I     e q u a l s

A
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